Related papers: Current Open Questions in Complete Mixability
In recent years, significant advances have been made in the design and analysis of fully dynamic maximal matching algorithms. However, these theoretical results have received very little attention from the practical perspective. Few of the…
We show that degrees containing a complete extensions of arithmetic have the random join property: they are the supremum of any random real they compute, with another random real. The same is true for the truth-table and weak truth-table…
Uncertainty is prevalent in engineering design, data-driven problems, and decision making broadly. Due to inherent risk-averseness and ambiguity about assumptions, it is common to address uncertainty by formulating and solving conservative…
We collect some open problems about minimal presentations of numerical semigroups and, more generally, about defining ideals and free resolutions of their semigroup rings and associated graded rings. We emphasize both long-standing problems…
The task of manipulating correlated random variables in a distributed setting has received attention in the fields of both Information Theory and Computer Science. Often shared correlations can be converted, using a little amount of…
The status of the problem of neutrino masses and mixing is shortly reviewed. Different schemes of mixing of (Dirac or Majorana) massive neutrinos are considered. The theory of neutrino oscillations in vacuum and in matter is presented.…
Rapid advances in computing technology over the past few decades have spurred two extraordinary phenomena in science: large-scale and high-throughput data collection coupled with the creation and implementation of complex statistical…
We contribute to the knowledge of the quantifier completions and their applications by using the language of doctrines. This algebraic presentation allows us to properly analyse the behaviour of the existential and universal quantifiers. We…
We synthesize and unify notions of regularity, both of individual sets and of collections of sets, as they appear in the convergence theory of projection methods for consistent feasibility problems. Several new characterizations of…
Since it first emerged in Wijsman's seminal work [29], the Wijsman topology has been intensively studied in the past 50 years. In particular, topological properties of Wijsman hyperspaces, relationships between the Wijsman topology and…
We give tight lower and upper bounds on the expected missing mass for distributions over finite and countably infinite spaces. An essential characterization of the extremal distributions is given. We also provide an extension to totally…
A multiscale theory of interacting continuum mechanics and thermodynamics of mixtures of fluids, electrodynamics, polarization and magnetization is proposed. The mechanical (reversible) part of the theory is constructed in a purely…
We introduce a general random model of a combinatorial optimization problem with geometric structure that encapsulates both linear programming and integer linear programming. Let $Q$ be a bounded set called the feasible set, $E$ be an…
This survey covers state-of-the-art Bayesian techniques for the estimation of mixtures. It complements the earlier Marin, Mengersen and Robert (2005) by studying new types of distributions, the multinomial, latent class and t distributions.…
We consider adjustable robust linear complementarity problems and extend the results of Biefel et al. (2022) towards convex and compact uncertainty sets. Moreover, for the case of polyhedral uncertainty sets, we prove that computing an…
One of the traditional applications of relation algebras is to provide a setting for infinite-domain constraint satisfaction problems. Complexity classification for these computational problems has been one of the major open research…
In this survey, we address mixing from the point of view of partial differential equations, motivated by applications that arise in fluid dynamics. We give an account of optimal mixing, loss of regularity for transport equations, enhanced…
This celebratory article contains a personal and idiosyncratic selection of a few open problems in discrete probability theory. These include certain well known questions concerning Lorentz scatterers and self-avoiding walks, and also some…
This paper provides fascinating connections between several mathematical problems which lie on the intersection of several mathematics subjects, namely algebraic geometry, approximation theory, complex-harmonic analysis and high dimensional…
A general piecewise (including pointwise) probability distribution with space-saving notation and its hierarchical particular cases are considered. The explicit closed-form normalization, expectation, and variance formulas along with the…